Well Test Simulation using Orthogonal Collocation

Abstract Welltesting is a flow of slightly compressible fluids in a porous media which is characterized by a set of nonlinear partial differential equations. Their solution is normally achieved analytically using Laplace transform or numerically through the use of numerical inverting methods of the Laplcace transform like Stehfest and Crump. Not all well test problems, however, are readily amenable to such treatment and an alternate approach like Orthogonal Collocation and Galerkin's methods are efficient and can be easily employed. Until now, the application of these techniques has been limited. The primary objective of this paper is to investigate the feasibility of using Orthogonal Collocation on well test of a slightly compressible fluid in an ideal radial flow system. A well test simulation that treats the reservoir as a non-homogeneous, irregularly bounded system has been developed. Since this work was primarily concerned with the feasibility of Orthogonal Collocation simulation, no attempt was made to study a wide spectrum of well test problems. However, a few typical applications are presented and some of the results are compared with those derived from analytical and numerical inversion. This study presents a new way to numerically simulate flow of slightly compressible fluid which is solved rigorously with wellbore storage and skin. This paper shows that the use of Orthogonal Collocation method is feasible and that, in many cases, it results in solutions that are more realistic than those resulted from numerical inversion of Laplace transform. There are, however, certain disadvantages. For example, oscillation of the pressure derivative which can be overcome by using Orthogonal Collocation on Finite Element (OCFE) in which programming effort are usually in excess of that required by a finite- difference or numerical Laplace inversion scheme. Even so, it is felt that the potential of the technique is sufficient justification for this work and for a continuing effort to apply it to well test simulation problems.